Question

A motorboat whose speed is 18 kilometre per hour in still water takes 1 hour more to go 24 kilometre upstream then to return down stream to the same spot find the speed of the stream.
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Answer 1

Given:

• Speed of the motorboat = 18 km/h.

Need to find:

• Speed of the stream.

Answer:

• 6 or -54

Step-by-step explanation:

Let the speed of the stream be x km/h.

Therefore,the speed of the boat upstream =(18-x) km/h and the speed of the boat downstream =(18+x) km/h.

The time taken to go upstream =distance/speed

$\large \implies{ \frac{24}{18 - x} hours}.$

Similarly,

The time taken to go downstream =distance/speed

$\large \implies{ \frac{24}{18 + x} hours}$

According to question,

$\large \implies{ \frac{24}{18 - x} - \frac{24}{18 + x} = 1}$

=> 24(18+x)- 24(18-x) = (18-x) (18+x)

$\small\implies{ \bold{ {x}^{2} + 48x - 324 = 0}}$

Using the quadratic formula,

We get

$\large\implies{x = \frac{ - 4 + \sqrt{ {48}^{2} + 1296} }{2} } \\ \large{ \implies{ \frac{ - 48 + \sqrt{3600} }{2} }} \\ \large{ \implies{ \frac{ - 48 + 60}{2} }} \\ \large \implies{ \bold{6 \: or \: - 54}}$

Since x is the speed of the stream,it cannot be negative. So, we ignore the root x = -54.

Therefore, x= 6 gives the speed of the stream as 6 km/h.